Question

Stabiliti,la fel ca in exemplele de la a) si b),care dintre numerele urmatoare este rational:
a)5 la puterea-2=1/5 la puterea 2
b)(radical7/3)la puterea-3=27/7radical7 nu apartineQ
c)4 la puterea-3
d)radical6 la puterea-2
e)(-2) la puterea-4
f)(2 radical2) la puterea-3
g)(radical5/radical11) la puterea-2
h)(2 radical3/3) la puterea-3

Answer 1

c)4 la puterea-3 = 4 ⁻ ³  = 1 / 4³  = 1 / 64  = 0,015625  ∈Q
d)radical6 la puterea-2 =√ 6⁻²  = 1 / √6² = 1 / √36 = 1 /6 =0,166666666666666666
= 0,1 (6) ∉ Q
e)(-2) la puterea-4     = ( -2 ) ⁻⁴ =  1 / ( -2 ) ⁴ = 1 / 16 = 0,0625∈ Q
f)(2 radical2) la puterea-3 = ( 2√2 ) ⁻ ³  = 1 / ( 2√2 ) ³ = 1 / 2³·√2³ = 1 /  8 ·2√2 =
= √2 / 32 ∉ Q
g)(radical5/radical11) la puterea-2 = (√5 / √7 )⁻ ²  = √7²  / √5² = 7 /5 =1,4 ∈ Q
h)(2 radical3/3) la puterea-3 = ( 2√3 /3 ) ⁻ ³  =  3³  / 2³·√3³ = 27 / 8·3√3 = 9 / 8·√3 =
= 9√3  / 8 ·3 = 3√3 / 8 ∉Q